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The existence of periodic solutions for a class of functional differential equations and their application. (English) Zbl 0793.34054

Summary: Four sufficiency theorems of existence of periodic solutions for a class of retarded functional differential equations are given. The result of these theorems is better than the well-known Yoshizawa’s periodic solution theorem. An example of application is given at the end.

MSC:

34K99 Functional-differential equations (including equations with delayed, advanced or state-dependent argument)
34C25 Periodic solutions to ordinary differential equations
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[1] Yoshizawa, T., Stability theory by Liapunov’s second method,Math. Soc. Japan, Tokyo, (1966). · Zbl 0144.10802
[2] Burton, T. A.,Volterra Integral and Differential Equations, Academic Press, New York, (1983), 286–287. · Zbl 0515.45001
[3] Li Xiao-ying, On the generalization of Massera’s and Yoshizawa’s theorems for periodic solutions,Journal of Northeast Normal University,1 (1987), 11–16. · Zbl 0642.34060
[4] Hale, J. K. and O. Lopes, Fixed point theorems and dissipative processes,J. Differential Equations,13 (1973), 391–402. · Zbl 0256.34069 · doi:10.1016/0022-0396(73)90025-9
[5] Zhao Jie-min, On the periodic solution problems of nonautonomous discret, periodic systems,Journal of Mathematical Research and Exposition,12, 3 (1992), 427-432. · Zbl 0767.34027
[6] Burton, T. A.,Stability and Periodic Solutions of Ordinary and Functional Differential Equations, Academic Press, (1985), 246–251. · Zbl 0635.34001
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